Accelerating GW calculations through machine-learned dielectric matrices

Mario G. Zauchner, Andrew Horsfield & Johannes Lischner 

npj Computational Materials9: 184 (2023).

10.1038/s41524-023-01136-y

Published online: 07 October, 2023

编辑概述

密度泛函理论（DFT）在计算电子基态性质方面取得了巨大成功。然而众所周知得是，当使用Kohn–Sham（KS）本征值进行计算时，通常会显著低估固体的带隙和分子的HOMO–LUMO能隙。为解决这一问题，我们通常采用GW方法对DFT KS能量进行自能修正。然而，GW方法需要进行大量的数值计算，并且与体系尺寸的标度关系并不理想，因而传统的GW计算通常限制在相对较小的体系上。GW方法中计算量最大的一步是相互作用密度–密度响应函数（DDRF）的计算，它与逆介电矩阵密切相关。为克服GW方法的这些限制，人们开发了模型DDRF（或模型介电函数）来加速GW计算。然而，难以将这些模型介电函数推广到孤立分子或纳米团簇等高度非均匀体系。在该工作中，来自英国伦敦帝国理工学院材料系的Johannes Lischner教授团队，开发了一种高效预测材料DDRF非局域响应函数的机器学习（ML）方法。DDRF的预测是一项艰巨的挑战：如果用平面波基组表示小型硅团簇的DDRF，即使选取适当的平面波截断能，其大小也将达到几十个GB。为解决这一问题，作者将DDRF分解为每个原子的贡献，从而可以使用ML技术进行预测。为确保ML模型包含DDRF合适的变换性质，他们开发了一种称为邻域密度矩阵（NDM）的描述符，其在旋转下与DDRF具有相同的变换方式。NDM与密集神经网络相结合，可以预测每个原子对DDRF的贡献。为评估该方法的准确性，作者将其应用于氢化硅团簇，发现该方法能够可靠地复现HOMO–LOMO能隙以及准粒子能级。这些进展为无序材料、液体、界面和纳米粒子等复杂系统的GW计算铺平了道路。

Editorial Summary

Accelerating GW calculations through machine-learned dielectric matrices

Density functional theory (DFT) has shown tremendous success in the calculation of electronic ground-state properties. However, it is well known that the band gaps of solids and the HOMO–LUMO gaps of molecules are often significantly underestimated when computed using Kohn–Sham (KS) eigenvalues. In order to remedy this issue, the GW method is often employed in which a self-energy correction to the DFT KS energies is computed. However, the large numerical effort required for GW calculations and the method’s unfavorable scaling with system size have traditionally restricted applications to relatively small systems. In GW method, the most expensive step is the computation of the interacting density–density response function (DDRF), which is closely related to the inverse dielectric matrix. To overcome these limitations, model DDRFs (or model dielectric functions) have been developed to accelerate GW calculations. However, it has proven difficult to generalize these model dielectric functions to highly non-uniform systems, such as isolated molecules or nano-clusters. In this work, a group led by Prof. Johannes Lischner from the Department of Materials, Imperial College London, developed a machine learning (ML) approach to efficiently predict non-local response functions, such as the DDRF, in materials. Predicting such quantities is a formidable challenge: for example, the DDRF of a small silicon cluster can be tens of gigabytes in size when represented on a plane-wave basis, even when a modest plane-wave cutoff is used. To address this problem, the authors introduced a decomposition of the DDRF into atomic contributions, which can be predicted using ML techniques. To ensure that the ML model appropriately incorporates the transformation properties of the DDRF, they developed a descriptor called neighborhood density–matrix (NDM), which transforms in the same way as the DDRF under rotations and is used in conjunction with a dense neural network to predict the atomic contributions to the DDRF. To assess the accuracy of this method, the authors applied it to hydrogenated silicon clusters and found that it reliably reproduces HOMO–LUMO gaps and quasiparticle energy levels. These advances pave the way for GW calculations of complex systems, such as disordered materials, liquids, interfaces, and nanoparticles.